Evaluation using a logical belief model

Evaluation of the game tree using a logical rather than a probabilistic belief model requires few changes to the design of the system. If the objective of the system is to choose the alternative with the best worst outcome (maximin), the weighted sum that is used with the probabilistic model can be replaced with a function that checks which of the three values of "believed", "disbelieved", and "possible" is taken at each chance node. Where the node proposition is disbelieved, the maximin value of the false branch is taken, where the proposition is believed, the maximin value of the true node is taken, and where the proposition is neither believed nor disbelieved, the minimum of the maximin values of both branches must be taken. The utility values obtained at the leaves of the game tree can either be continuous, or some ordinal representation of plan success and failure, for example 1 for success and 0 for failure. It is possible to transform a logical belief model to a probabilistic one so that it can be used with the current design for the belief model. One way is to use probability values of $1$, $1/2$, and 0 to represent the logical states of believed, neither, and disbelieved. These values can then be checked when the maximin evaluation function is applied at a chance node.

Figure 3.3: Evaluation example for a question and answer game tree